Telecommunications systems, cable television systems and data communication networks may use optical networks to rapidly convey large amounts of information between remote points. In an optical network, information may be conveyed in the form of optical signals through optical fibers. Optical fibers may comprise thin strands of glass capable of communicating the signals over long distances with very low loss. Optical networks often employ modulation schemes to convey information in the optical signals over the optical fibers. Such modulation schemes may increase the amount of information that can be conveyed. For example, in quadrature amplitude modulation (QAM), the information carried by the optical signal may be conveyed by modulating both the amplitude and phase of the carrier wave. QAM signals may be represented using a complex plane with real and imaginary axes on a constellation diagram. The points on the constellation diagram represent symbols carrying information and may be positioned with uniform angular spacing around the origin of the diagram. As the number of points on constellation diagram increases, the amount of information that can be carried per symbol increases. As a result, the overall amount of information that can be conveyed increases.